Several years​ ago, two companies merged. One of the concerns after the merger was the increasing burden of retirement expenditures

QUESTION

Several years​ ago, two companies merged. One of the concerns after the merger was the increasing burden of retirement expenditures. An effort was made to encourage employees to participate in the​ 401(k) accounts.​ Nationwide, ​% of eligible workers participated in these accounts. The accompanying data table contains responses of employees of the company when asked if they were currently participating in a​ 401(k) account. Complete parts a through d.

No is 11 Yes is 19

a. Determine the sample proportion of company workers who participate in​ 401(k) accounts. The sample proportion is . ​(Round to three decimal places as​ needed.)

b. Determine the sampling error if in reality the company workers have the same proportion of participants in​ 401(k) accounts as does the rest of the nation. The error is . ​(Round to three decimal places as​ needed.)

c. Determine the probability that a sample proportion at least as large as that obtained in the sample would be obtained if the​ company's workers have the same proportion of participants in the​ 401(k) accounts as does the rest of the nation. The probability is . ​(Round to four decimal places as​ needed.)

d. Does it appear that a larger proportion of company workers participate in​ 401(k) accounts than do the workers of the nation as a​ whole? Support your response. ▼ Yes, or No, because there is a ? % chance of obtaining a sample proportion greater than the one calculated in part a if the population proportion is ​%. ​(Round to the nearest percent as​ needed.)